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Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.


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Journal ArticleDOI
TL;DR: The effects of a fuzzy logic controller saturation gives rise to a universal nonlinearity for this type of controller, which causes some pathological behaviors such as oscillations or unstable limit cycles to occur.

41 citations

Journal ArticleDOI
TL;DR: In this article, nonlinear stability analyses of control surface flutter were conducted on a threedegree-of-freedom typical-section airfoil with free play about the control surface hinge line.
Abstract: Results are presented from nonlinear stability analyses of control surface flutter that were conducted on a threedegree-of-freedom typical-section airfoil with free play about the control surface hinge line. The describing function (harmonic-balance) method has been used to predict response amplitudes, and a locally parameterized continuation method has been used to track all flutter modes. Themethodology is directly applicable to systems with unsteady air loads expressed in either the frequency or time domains. Both stable and unstable limit cycles have been identified. Limit cycle stability has been assessed by examining the change in growth rate due to amplitude perturbations at a given velocity. Limit cycle amplitudes predicted by the describing functionmethod,with frequency-domain unsteady aerodynamics, are shown to compare very well with the magnitudes of time-history responses obtained by direct integration of the equations of motion, using rational function approximation time-domain aerodynamics. Results from these nonlinear analyses are compared with analytical and experimental results of similar analyses from the open literature.

40 citations

Proceedings ArticleDOI
04 Jun 1997
TL;DR: This paper addresses the zero-input stability of control systems utilizing so-called Clegg integrators and provides a definitive stability condition for second-order plants as well as providing preliminary results for higher- order plants.
Abstract: We consider control systems utilizing so-called Clegg integrators. A Clegg integrator is a linear integrator with reset mechanism whose describing function 1.62//spl omega/ /spl ang/-38.1/spl deg/ has magnitude slope equivalent to that of a linear integrator, but with 51 less degrees of phase lag. The potential advantages of using Clegg integrators to meet stringent design specifications has been demonstrated in the literature, however, stability analyses are missing. This paper addresses the zero-input stability of such control systems and provides a definitive stability condition for second-order plants as well as a providing preliminary results for higher-order plants.

40 citations

Journal ArticleDOI
01 Jul 1956
TL;DR: The method can be considered as an extension of the describing-function technique with a correspondingly wider field of application for analysing four different types of problem arising in feedback systems containing one simple-type amplitude non-linearity.
Abstract: A new method is presented for the frequency-response analysis of non-linear elements. This involves evaluating the gain of one of the frequency components in passing through the non-linear element when the input to the element consists of two sinusoidal waves of differing amplitudes, phases and frequencies. A cubic characteristic is analysed fully as an example. The paper describes the use of this method for analysing four different types of problem arising in feedback systems containing one simple-type amplitude non-linearity. The method can be considered as an extension of the describing-function technique with a correspondingly wider field of application.

40 citations

Journal ArticleDOI
TL;DR: In this paper, a first-order harmonic balance approach based on describing function representations for the flame response is proposed to investigate the dynamics of thermoacoustic systems with multiple linearly unstable modes, and conditions for the existence and stability of single or multi-mode steady-state oscillations.
Abstract: We investigate the dynamics of thermoacoustic systems with multiple linearly unstable modes. If a linear analysis reveals more than one mode with positive growth rate, nonlinear methods have to be used to determine the existence and stability of steady-state oscillations. One possible way to engage this problem is a first-order harmonic balance approach based on describing function representations for the flame response. In contrast to the case of a single unstable mode, the nonlinearity output to multiple sinusoidal components with different frequencies and amplitudes has to be known. Based on this approach, we present conditions for the existence and stability of single- or multi-mode steady-state oscillations. We apply this method to a thermoacoustic model system having two linearly unstable modes. By varying one of the system parameters, we find stable and unstable single-mode steady-states as well as unstable simultaneous oscillations. Associated with the stability of the single-mode limit cycles, we...

40 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847